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3-065-UpDown-ModelingScenario

Author(s): Brian Winkel

SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations

Keywords: terminal velocity Newton's Second Law of Motion velocity motion apex

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Abstract

Resource Image We model the height of a launched object which is subject to resistance proportional to velocity during its flight. We ask questions about the motion as well, e.g., highest point or apex and terminal velocity.

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Resource Type
Differential Equation Type
Technique
Qualitative Analysis
Application Area
Course
Course Level
Lesson Length
Technology
Approach
Skills
Key Scientific Process Skills
Assessment Type
Pedagogical Approaches
Vision and Change Core Competencies - Ability
Principles of How People Learn
Bloom's Cognitive Level

Description

An object of mass m is launched vertically upward from ground level with an initial velocity of v0 and is slowed down by air resistance in the form of a force proportional to its velocity, i.e. k*v.

Draw a free body diagram of the forces acting on the object.

Use Newton's Second Law of Motion to build a differential equation of motion for its distance from the ground, s(t) in meters at time t in seconds.

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Authors

Author(s): Brian Winkel

SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations

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